A criterion for the properness of the K-energy in a general Kahler class

2013/11/05 by Haozhao Li, Li, Haozhao, Yalong Shi +3 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1311.1032

openalex publication_date 2013/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we give a criterion for the properness of the K-energy in a general Kahler class of a compact Kahler manifold by using Song-Weinkove's result. As applications, we give some Kahler classes on ℂℙ²#3 ℂℙ² and ℂℙ²#8 ℂℙ² in which the K-energy is proper. Finally, we prove Song-Weinkove's result on the existence of critical points of J functional by the continuity method.

Citations

• Stable Pairs and Coercive Estimates for The Mabuchi Functional
• Alpha invariants and K-stability for general polarisations of Fano varieties
• On a class of fully nonlinear elliptic equations on Hermitian manifolds

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• Geodesic rays and stability in the cscK problem

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